Ask an Economist is back and just in time for 11 Little Roosters! Some of you may remember last year's 10 Little Roosters edition where I broke down the odds of correctly guessing the murderer and survivor, and the subsequent post mortem of your guesses (Part 1 and 2). Now, we're dealing with new rules and a different set of circumstances. Time to blow the dust of ye olde modeels and get cracking.
This round, instead of guessing a victim and murder weapon, we'll be guessing which organization will eliminate another. No more worrying about endless permutations of weapons assigned to victims. That does make the math a little easier and your odds better.
We'll break down the odds in two likely scenarios: one is complete random guessing of both victim and killer. The other is assuming that you were able to determine (with confidence) either the victim or killer. That leaves the random guessing only of the remaining unknown. With that said, let's get to the numbers!
At the end of Episode 1, we have 10 remaining organizations. That means, if we were randomly guessing, 90 possible combinations of killer and victim (1.1% chance) to choose from. If we, say, use the Haywood files and determine exactly who'll be the victim, we then know that there are only 9 possible killers (11.1%). That makes the guessing much better. The table below shows the odds (and percentage chance) of guessing the correct victim and killer each episode.
As expected, the odds get better the fewer organizations that are left remaining. Despite those easier odds, getting it correct from the very beginning is tough. How tough you (and @Steffie) would ask? If we were randomly guessing, the odds of correctly guessing each week is ....
1 in 1.32 Trillion!
Yep. Believe it or not, those are much better odds than those from 10 Little Roosters. That seems a tad beyond the hopes and dreams of us players. What about if we use parts of the Haywood Files and figure out at least one of the two unknowns each week? Well that's only a paltry 1 in 362,880 chance. No sweat, right?
Of course, @JoshtheFlanagan was kind enough to hide many Haywood Files in each episode. Using them, we can reduce those odds even further!
A question an economist gets asked most often is "so what who cares [about those odds]." Those odds should serve as a reminder of how important those Haywood Files are. Without them, you'll be swimming in a sea of uncertainty; at the mercy of the winds of statistical unlikelihoods. Perhaps take a little extra time to make sure you get those Haywood Files.